第51届国际物理奥林匹克竞赛理论第三题介绍与解答

SOLUTION TO THE THIRD PROBLEM OF THE 51th INTERNATIONAL PHYSICS OLYMPIAD THEORETICAL EXAM

第51届国际物理奥林匹克竞赛理论试题共有三道题,第一题关于力学热学,第二题以电磁学为主,本文介绍的第三题是关于波动光学与量子物理。该题利用简化的量子一维势阱模型来估算分子的能级结构和光谱性质,以及利用波的叠加产生光学晶格来束缚原子以实现玻色爱因斯坦凝聚。题目将光学和量子物理紧密结合,在近年来的国际奥赛中较为新颖,因而在本文做一个详细的介绍与解答。

There were three problems in the theoretical exam of the 51^(th) international Physics Olympiad which was hosted by Lithuania in July,2021.The first problem is on mechanics and thermal physics;the second is on electro-magnetic.We discuss the third problem which is about optics and quantum physics in this paper.The problem applies simple model of one-dimension potential well to estimate the energy level and spectral property of molecules;as well as trapping atoms with optical lattice to realize Bose-Einstein Condensation.The problem combines wave optics and quantum physics in a coherent way,which is quite novel in recent international Olympiads.We thus present a detailed discussion and solution on the problem in this article.